C4 chapter 3 - the Binomial Theorem

We learnt about the binomial theorem back in C2 chapter 5, but in this unit we extend that to allow us to find expansions of binomials to powers other than positive whole-numbers.

C4 section 3.1

You need to be able to recall and use the standard binomial expansion from C2 chapter 5.
This introduction to the chapter revises a little of that and sets us off thinking about what happens when the power is not a positive whole number:

C4 chapter 3 Binomial Theorem intro.jnt

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C4 chapter 3 Binomial Theorem intro.pdf

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You need to know:

Examples:

C4 Exercise 3A

• C4 Exercise 3A worked solutions: on the way (06.01.14)
• Questions similar to this exercise:

C4 section 6.2

Use the Binomial Theorem to find an infinite expansion of
$\displaystyle \dfrac{1}{(1-x)^2}$
and note the conditions on x for this to work.
Hold on to that somewhere. In a moment look at the video below about a rather interesting and curious fact about
$\displaystyle \dfrac{1}{998001}$
But before you hit play, why not ask Wolfram¦alpha to evaluate that fraction as a decimal and use the 'show more digits' function?